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Restructuring and Integration Expense - Schedule of Restructuring Expenses by Segment (Details) - USD ($) $ in Millions | 12 Months Ended
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May 31, 2025 | Jun. 01, 2024 | Jun. 03, 2023
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | $ 14.8 | $ 30.8 | $ 34.4
Corporate |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 0.0 | 0.0 |
Knoll Integration |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 28.3 | 23.5 | $ 18.0
Knoll Integration | Corporate |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 0.0 | 0.1 |
2025 Restructuring Plan |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 14.8 |  |
2024 Restructuring Plan |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 0.0 | 30.8 |
North America Contract | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 9.8 | 25.3 |
North America Contract | Knoll Integration | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 24.8 | 22.6 |
International Contract | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 3.3 | 3.4 |
International Contract | Knoll Integration | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 3.2 | 0.3 |
Global Retail | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | 1.7 | 2.1 |
Global Retail | Knoll Integration | Operating Segments |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Restructuring expenses | $ 0.3 | $ 0.5 |

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